Partial average cross‐weight evaluation for ABC inventory classification

• Author: Giannis Karagiannis
• Date: 01 May 2021
• Published date: 01 May 2021
• DOI: http://doi.org/10.1111/itor.12594

Intl. Trans. in Op. Res. 28 (2021) 1526–1549

DOI: 10.1111/itor.12594

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

Partial average cross-weight evaluation for ABC

inventory classification

Giannis Karagiannis∗

Department of Economics, University of Macedonia, 156 Egnatia Str., Thessaloniki, 54006 Greece

E-mail: karagian@uom.edu.gr [Karagiannis]

Received 27 October 2017; receivedin revised form 27 July 2018; accepted 20 August 2018

Abstract

In this paper, we propose an alternative overall measure, inspired by the notion of average cross-efficiency,

which summarizes achievements across different descending ordering schemes regarding the relative impor-

tance of the considered indicators in the Ng model. The proposed overall measure is equal to the arithmetic

average of the maximum partial averages across all possible descending ordering schemes. It can also be

obtained using the average (across ordering schemes) of the estimated multipliers. We apply the proposed

measure to the ABC inventory classification problem, and we compare our results with those by four in-

formation theory based methods that may be used for the same purpose, namely the Shannon entropy,

distance-based, weighted least-square dissimilarity, and maximizing deviation methods.

Keywords:composite indicators; descending ordering schemes; overall measure; ABC inventory classification

1. Introduction

In performance evaluation literature, the performance of individualdecision-making units (DMUs)

may be evaluated under three appraisal schemes: self-appraisal, peer appraisal, or preference ap-

praisal. Self-appraisal refers to the case that each evaluated DMU is allowed to choose its own

“value system,” by means of the weights attached to each performance indicator, in order to show

the best possible light relative to other DMUs included in the assessment.1Each evaluated DMU

can exaggerate its own advantages and at the same time downplay its own weakness to obtain the

maximal possible evaluation score. Data envelopment analysis (DEA), introduced by Charnes et al.

(1978), is the main operation research tool for conducting self-appraisal performance evaluation.

On the other hand, peer appraisal gives the right to every DMU to have a “say” about the evalu-

ation of the other DMUs. In particular, each DMU takes into account the “value system” of all

∗Corresponding author.

1In some cases, performance indicators takethe form of inputs and outputs as in productive efficiency analysis, while in

other cases they reflect different aspects of performance as in the construction of composite indicators.

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2018 The Authors.

International Transactionsin Operational Research C

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G. Karagiannis / Intl. Trans. in Op. Res.28 (2021) 1526–1549 1527

evaluated units (included itself) in assessing its own performance. Since each “value system” re-

sults in a different evaluation score, performance is gauged by the average of the efficiency scores

obtained using all DMUs’ self-appraisal weights (see Sexton et al., 1986; Doyle and Green, 1994),

which is called average cross-efficiency. Lastly, in the case of preference appraisal, aprioriinforma-

tion provided by experts, stakeholders, or policy makers is incorporated into the evaluation process

by means of a predetermined “value system.” Their preferences about the importance of the con-

sidered performance indicators are reflected in a set of restrictions that reduce the weight flexibility

of self-appraisal DEA (Dyson et al., 2001; Angulo-Meza and Lins, 2002). These restrictions may

either take the form of numerical limits on the weights of the considered performance indicators or

provide a ranking of their relative importance, with the latter having the advantage of being simple

and intuitive (Joro and Viitala, 2004).

Sometimes, however, experts, stakeholders, or policy makers cannot reach a consensus about the

relative importance of the considered performance indicators. This turns into an issue as long as

it affects the estimated scores and/or the final ranking of DMUs. Then, the choice of a particular

ordering scheme becomes difficult and debatable especially if there is no apriorireason to weight

the opinion of an expert, stakeholder or policy maker more than another’s. In such cases, one may

either use all acceptable ordering schemes to examine the extent of changes (if any) in the final

ranking of the evaluated DMUs or alternatively, may try to obtain an overall performance measure

summarizing achievements across different ordering schemes. A similar situation may arise in a

different occasion: for example, when an analyst conducts a sensitivity analysis on the resulting

efficiency scores by examining the entire set of possible ordering schemes regarding the importance

of the considered performance indicators. Then, it may also be useful to end up with a single metric

that reflects performance under all different norms or “value systems.”

The problem of deriving such an overall or synthetic perfor mance measure has been handled

so far by information theory methods. In particular, Fu et al. (2015) and Zheng et al. (2017) used

Shannon entropy to aggregate a DMU’s evaluation scores obtained under alternative ordering

schemes regarding the importance of the considered performance indicators, while for the same

purpose Fu et al. (2016) and Cao et al. (2016) employed a distance-based method, and Wu et al.

(2018) the weighted least-square dissimilarity method of Wang and Wang (2013).2Both these are

purely data-driven methods trying to exploit the infor mation of the data itself. For example, the

entropy method rateshigher for overall performance the preference-appraisal evaluation scores with

the relatively larger variation across DMUs, and consequently, assigns to them a higher aggregation

weight. If an ordering scheme results in evaluation scores that have almost no variation across

DMUs, then its aggregation weight tends to 0. On the other hand, the distance-based method

rates higher for overall performance the preference-appraisal evaluation scores with the smaller

deviations from the mean and as a result, it assigns to them a higher aggregation weight.

The objective of this paper is to propose an alternative overall or synthetic performance measure

rooted to performance evaluation rather than to information theory. In particular, the proposed

measure is inspired by the notion of average cross-efficiency. The difference is however that in

preference-appraisal case, we consider all possible ordering schemes as reflecting the different

“value systems” while the entire set of DMUs determines the different “value systems” in peer

2The distance-based method has been employed previously by Wu et al. (2012) for aggregating cross-efficiencies. It may

be considered as a modification of the Wangand Wang (2013) weighted least-square deviation approach.

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2018 The Authors.

International Transactionsin Operational Research C

2018 International Federation of OperationalResearch Societies